Tài liệu Modeling of Data part 1 pptx

... 15 .1 Least Squares as a Maximum Likelihood Estimator 657 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge ... 19 68, Mathematical Handbook for Scientists and Engineers , 2nd ed. (New York: McGraw-Hill), Chapters 18 19 . 15 .1 Least Squares as a Maximum Likelihood Estimator Suppose that we are fit...

Ngày tải lên: 15/12/2013, 04:15

... W.E. 19 43, Statistical Adjustment of Data (New York: Wiley), reprinted 19 64 (New York: Dover). [1] Jefferys, W.H. 19 80, Astronomical Journal , vol. 85, pp. 17 7 18 1; see also vol. 95, p. 12 99 (19 88). ... x1, float x2, float tol); int j; float swap,amx,amn,varx,vary,ang[7],ch[7],scale,bmn,bmx,d1,d2,r2, dum1,dum2,dum3,dum4,dum5; xx=vector (1, ndat); yy=vector (1, ndat); 670 Cha...

Ngày tải lên: 15/12/2013, 04:15

... 4.72 5.89 7.04 90% 2. 71 4. 61 6.25 7.78 9.24 10 .6 95.4% 4.00 6 .17 8.02 9.70 11 .3 12 .8 99% 6.63 9. 21 11. 3 13 .3 15 .1 16.8 99.73% 9.00 11 .8 14 .2 16 .3 18 .2 20 .1 99.99% 15 .1 18.4 21. 1 23.5 25.7 27.8 These ... Plugging (15 .6.2) into (15 .6 .1) and using the fact that [C] and [α] are inverse matrices of one another, we get c = δa 1 /C 11 and ∆χ 2 ν =(δa 1 ) 2...

Ngày tải lên: 15/12/2013, 04:15

... *arr,d,sum=0.0; arr=vector (1, ndatat); for (j =1; j<=ndatat;j++) arr[j]=yt[j]-b*xt[j]; if (ndatat & 1) { aa=select((ndatat +1) >> ;1, ndatat,arr); } else { j=ndatat >> 1; aa=0.5*(select(j,ndatat,arr)+select(j +1, ndatat,arr)); } abdevt=0.0; for ... y(x i )}∼ 1 1+ 1 2  y i −y(x i ) σ i  2 (15 .7.9) 15 .7 Robust Estimation 703 Sample page from NUMERICAL RECIPES IN...

Ngày tải lên: 15/12/2013, 04:15

... into (15 .1. 4), so that the maximum likelihood 658 Chapter 15 . Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 ... minimum, 0= N  i =1  y i − y(x i ) σ 2 i  ∂y(x i ; a k ) ∂a k  k =1, ,M (15 .1. 7) Equation (15 .1. 7) is, in general, a set of M nonlinear equations for the M unkno...

Ngày tải lên: 15/12/2013, 04:15

... Define t i = 1 σ i  x i − S x S  ,i =1, 2, ,N (15 .2 .15 ) and S tt = N  i =1 t 2 i (15 .2 .16 ) Then, as you can verify by direct substitution, b = 1 S tt N  i =1 t i y i σ i (15 .2 .17 ) a = S y − S x b S (15 .2 .18 ) 15 .2 Fitting Data ... 15 .2.2). For unweighted data (all σ i =1) , that relation is χ 2 = (1 r 2 )NVar (y 1 y N ) (15 .2 .13 ) where NVar (y 1 y N )≡ N...

Ngày tải lên: 15/12/2013, 04:15

... combinations of the columns of V. In fact, equation (15 .4 .17 ) can be written in a form displaying these errors as a =  M  i =1  U (i) · b w i  V (i)  ± 1 w 1 V (1) ±···± 1 w M V (M) (15 .4 .18 ) Here ... call 1- 800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). X 1 (x 1 ) σ 1 x 1 X 2 (x 1 ) σ 1 . . . X M (x 1...

Ngày tải lên: 15/12/2013, 04:15

... Initialization. atry=vector (1, ma); beta=vector (1, ma); da=vector (1, ma); for (mfit=0,j =1; j<=ma;j++) if (ia[j]) mfit++; oneda=matrix (1, mfit ,1, 1); *alamda=0.0 01; mrqcof(x,y,sig,ndata,a,ia,ma,alpha,beta,chisq,funcs); ochisq=(*chisq); for ... the value χ 2 of a fit between a set of data points x [1 ndata] , y [1 ndata] with individual standard deviations sig [1 ndata] , and...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 13/12/2013, 20:15

... { sig[k][l]=sig[k -1] [l +1] +(alpha[l -1] -a[k-2])*sig[k -1] [l]- b[k-2]*sig[k-2][l]+beta[l -1] *sig[k -1] [l -1] ; } a[k -1] =alpha[k -1] +sig[k][k +1] /sig[k][k]-sig[k -1] [k]/sig[k -1] [k -1] ; b[k -1] =sig[k][k]/sig[k -1] [k -1] ; } free_matrix(sig ,1, 2*n +1, 1,2*n +1) ; } As an example of the use of orthog, ... for k =1, 2, ,N − 1, compute σ k,l = σ k 1, l +1 − (a k 1 − α l )σ k...

Ngày tải lên: 15/12/2013, 04:15